Regularity for nonlocal problems with non-standard growth

Chaker J, Ki M, Weidner M. Regularity for nonlocal problems with non-standard growth. Calculus of Variations and Partial Differential Equations . 2022;61(6): 227.We study robust regularity estimates for local minimizers of nonlocal functionals with non-standard growth of (p, q)-type and for weak solutions to a related class of nonlocal equations. The main results of this paper are local boundedness and Holder continuity of minimizers and weak solutions. Our approach is based on the study of corresponding De Giorgi classes